Before our server went in to a bad state, this line was disappearing in the logs for almost 5 days.

Would like to know whether the absence of this line means the JVM did not perform the GC activity for those 5 days or is it like Weblogic not necessarily need to log this line but GC activity would be carried out by JVM periodically in the background?

The garbage collection cycles in the JVM and the report from the WebLogic GC Monitor are two different things. The JVM will go on executing GC cycles whether the GC Monitor runs at all. I have no idea why you wouldn't have seen this report in the logs.

Also note that if you're concerned that the free memory gets to such a low level, if you're not using a generational collector, or you end up with a very large young generation, it's perfectly natural for the free memory to get very low, just before the GC that bumps it way up to 60-70 % free.